Yes, you can pay 3 mana to stick a counter back onto Iceberg before you untap, and sure, you can do cute things to reduce costs or repopulate your ice counters with Rimefeather Owl, Zirda, the Dawnwaker, and proliferate triggers
Where Warrant suffers relative to other options is against utility creatures, mainly mana creatures like Llanowar Elves and Incubation Druid, but most control players are happy to see those cards because they can focus their answers on the big threats with little threat of dying from the cheap cards
That being said, Rat decks have existed for a while, with cards like Marrow-Gnawer turning a single Rat into an army
As white typically runs creature buffs this has good synergies within the kinds of places you might want it
These include cards like Blood Tyrant (drain, +1/+1 counters), Dragonmaster Outcast (5/5 dragon tokens), Indulgent Tormentor (draw, drain), Sin Prodder (draw, drain), Thassa (scry), Twilight Prophet (draw, drain), Wildfire Devils (reanimate spells), Skyline Despot (5/5 Dragon tokens), Avarice Amulet (draw), Extravagant Replication (clone), and many many more
Part of the charm of Disney Lorcana is how the aspects of each card (the artwork, the abilities, and the stats) all combine to tell the story of a Disney fans favorite glimmer
